SOLUTION: A man is twice as old as his son.10years ago he was three times as old.how old will his son be in 5years time?

Question 592782: A man is twice as old as his son.10years ago he was three times as old.how old will his son be in 5years time?
Answer by ntnk(54) (Show Source): You can put this solution on YOUR website!
Let's turn the statements you give above into equations. Let's call the man's age M and the son's age S.
(1) A man is twice as old as his son: M = 2 * S.
Since the man's age today is M and the son's age is S, this means this means that 10 years ago, the man's age was M-10 and the son's age was S-10.
(2) 10years ago he was three times as old: M-10 = 3 * (S-10).
Now we can solve for the man's age an his son's age by substitution. We can plug the first equation (M=2*S) into the second one so that
M - 10 = 3 * (S-10)
becomes
2*S - 10 = 3 * (S-10).
Now we can solve for S. First use the distributive property on the right-hand side to get
2*S - 10 = 3*S - 30
Now add 30 to both sides to get
2*S + 20 = 3*S
and subtract 2*S from both sides to get
20 = S.
This is the age of the son today. The question asks how old the son will be in 5 years, so the answer must be 20+5 = 25 years old.
Now let's check. We think the son is 20 years old today. Since the man is twice as old, the man must be 40. Ten years ago, the man was 30 and the son was 10. Therefore the man was 3 times as old as the son ten years ago, so everything checks out. I hope this helps!
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